(1+cos20°)/2sin20°-sin10°(cot5°-tan5°)
=(1+cos20°)/4sin10°cos10°-sin10°(cot5°-tan5°)
=2cos10°/4sin10°-2sin5°cos5°(cot5°-tan5°)
=cos10°/2sin10°-2((cos5°) ＾2 -(sin5°)＾2)
=cos10°/2sin10°-2cos10°
=(cos10°-4sin10°cos10°)/2sin10°
=(sin80°-2sin20°)/2sin10°
=((sin80°-sin20°)-sin20°)/2sin10°
=(2cos50°sin30°-sin20°)/2sin10°
=(sin40°-sin20°)/2sin10°
=2cos30°sin10°/2sin10°
=cos30°
=√3/2